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Differentiation matrices for univariate polynomials
- Source :
- Numerical Algorithms. 83:1-31
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- Differentiation matrices are in wide use in numerical algorithms, although usually studied in an ad hoc manner. We collect here in this review paper elementary properties of differentiation matrices for univariate polynomials expressed in various bases, including orthogonal polynomial bases and non-degree-graded bases such as Bernstein bases and Lagrange and Hermite interpolational bases. We give new explicit formulations, and new explicit formulations for the pseudo-inverses which help to understand antidifferentiation, of many of these matrices. We also give the unique Jordan form for these (nilpotent) matrices and a new unified formula for the transformation matrix.
- Subjects :
- Hermite polynomials
Applied Mathematics
Numerical analysis
MathematicsofComputing_NUMERICALANALYSIS
Univariate
010103 numerical & computational mathematics
01 natural sciences
010101 applied mathematics
Algebra
Nilpotent
Transformation matrix
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Orthogonal polynomials
Theory of computation
0101 mathematics
Algebra over a field
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 83
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........ef1d9e8a55f41bbba369905896f920f9